What is the integral of e^{xy} ?

The integral of e^{xy} is 1/y e^{yx}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{xy}

\int e^{x y} d x

\frac{1}{y} e^{y x} + C

Solution steps

\int e^{x y} d x

Apply u-substitution

: \int \frac{e ^{u}}{y} d u

= \int \frac{e ^{u}}{y} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{y} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{y} e^{u}

Substitute back

u = y x

= \frac{1}{y} e^{y x}

Add a constant to the solution

= \frac{1}{y} e^{y x} + C

f (x) = \frac{1 + 16 x ^{2}}{( 4 x ) ^{3}}

y^{^{''}} - y^{^{'}} = 0, y (0) = 10

\int \frac{4}{3 - x} d x

\frac{\partial}{\partial x} (x^{2} - x y - y^{2})

\frac{d y}{d x} = x y + 3 x + 5 y + 15